Optical microcavity resonator sensor

ABSTRACT

An optical resonator accelerometer includes an optical microcavity and an optical waveguide that evanescently couples light incident on an input end of the waveguide core into the high-Q WGMs of the microcavity at a coupling efficiency of over 99%. The waveguide includes a waveguide core, and a multi-layer dielectric stack that has alternating high and low refractive index dielectric layers. The reflectivity of the dielectric stack is sufficient to isolate the waveguide core and the microcavity from the substrate. A flexure has a first end mounted to the substrate, and a second end arranged to interact with said optical microcavity. The flexure is responsive to an inertial input to cause a change in the coupling geometry between the microcavity and the optical waveguide.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] Not Applicable

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] Not Applicable

REFERENCE TO MICROFICHE APPENDIX

[0003] Not Applicable

FIELD OF THE INVENTION

[0004] The present invention relates to optical sensors, and inparticular to highly sensitive, integrated microcavity-waveguide sensor.

BACKGROUND OF THE INVENTION

[0005] During the past few years, a substantial amount of research hasbeen performed in the field of optical microcavity physics, in order todevelop high cavity-Q optical microcavity resonators. In general,resonant cavities that can store and recirculate electromagnetic energyat optical frequencies have many useful applications, includinghigh-precision spectroscopy, signal processing, sensing, and filtering.Many difficulties present themselves when conventional planartechnology, i.e. etching, is used in order to fabricate high qualityoptical resonators, because the surfaces must show deviations of lessthan about a few nanometers. Optical microcavity resonators, on theother hand, can have quality factors that are several orders ofmagnitude better than typical surface etched optical resonators, becausethese microcavities can be shaped by natural surface tension forcesduring a liquid state fabrication. The result is a clean, smooth silicasurface with low optical loss and negligible scattering. Thesemicrocavities are inexpensive, simple to fabricate, and are compatiblewith integrated optics.

[0006] Optical microcavity resonators have quality factors (Qs) that arehigher by several orders of magnitude, as compared to otherelectromagnetic devices. Measured Qs as large at 10¹⁰ have beenreported, whereas commercially available devices typically have Qsranging from about 10⁵ to about 10⁷. The high-Q resonances encounteredin these microcavities are due to optical whispering-gallery-modes (WGM)that are supported within the microcavities.

[0007] As a result of their small size and high cavity Q, interest hasrecently grown in potential applications of microcavities to fields suchas electro-optics, microlaser development, measurement science, andspectroscopy. By making use of these high Q values, microsphericcavities have the potential to provide unprecedented performance innumerous applications. For example, these microspheric cavities may beuseful in applications that call for ultra-narrow linewidths, longenergy decay times, large energy densities, and fine sensing ofenvironmental changes, to cite just a few examples.

[0008] In order for the potential of microcavity-based devices to berealized, it is necessary to couple light selectively and efficientlyinto the microspheres. Since the ultra-high Q values of microcavitiesare the result of energy that is tightly bound inside the cavity,optical energy must be coupled in and out of the high Q cavities,without negatively affecting the Q. Further, the stable integration ofthe microcavities with the input and output light coupling media shouldbe achieved. Also, controlling the excitation of resonant modes withinthese microcavities is necessary for proper device performance, butpresents a challenge for conventional waveguides.

[0009] Typically, good overall performance is gained by accessing theevanescent field in a waveguide. Also, only waveguide structures provideeasy alignment and discrete, clearly defined ports. Because of cavityand waveguide mode leakage into the substrate and into the modes withinthe fiber cladding, power extraction from the input optical radiationhas proved to be inefficient for conventional planar waveguides,however.

[0010] U.S. patent application Ser. No. ______ (identified by AttorneyDocket Nos. CSLL-162 and hereby incorporated by reference)(hereinafterthe “CSLL-162” application) discloses a highly efficient and robustmechanism for coupling optical microcavity whispering-gallery modes intointegrated optical waveguide chips. SPARROW (Stripline PedestalAntiresonant Reflecting Waveguides) are used to achieve verticalconfinement and substrate isolation through a highly reflective stack ofalternating high and low refractive index dielectric layers. Q-values ofover 10⁹, and coupling efficiencies of over 99% have been observed.

[0011] Because of the ability of SPARROW waveguide chips to exciteresonant modes having unprecedentedly high Q-values in opticalmicrocavities, it is desirable to implement SPARROW waveguide chips insensing applications, so as to increase the resolution and dynamic rangein these applications.

SUMMARY OF THE INVENTION

[0012] The present invention is directed to the implementation of awaveguide-coupled optical microcavity resonator for sensingapplications. In particular, a SPARROW (Stripline Pedestal AntiresonantReflective Optical Waveguide) optical chip structure is used toevanescently couple light into an optical microcavity at very highefficiencies, approaching 100%. An input, for example an external forceor a change in an environmental condition such as temperature, causesthe microcavity to move, and causes a change in the coupling geometrybetween the microcavity and the optical waveguide. In one embodiment,the change in coupling geometry is caused by a displacement of themicrocavity in response to the inertial input, the displacementresulting in a change in the coupling gap between the microcavity andthe waveguide. Using a sensor constructed in accordance with the presentinvention, a resolution limit of about 10⁻¹⁷m and a dynamic range ofabout 10¹⁰ can be reached for the sensing of acceleration, representingan improvement over prior art accelerators of several orders ofmagnitude.

[0013] An optical resonator sensor, constructed in accordance with thepresent invention, includes a substrate, a SPARROW optical waveguidedisposed on the substrate, an optical microcavity, and a flexure. Theoptical microcavity is a fused silica microcavity, capable of supportinghigh Q-factor whispering-gallery-modes (WGM). Photons within these modesare strongly confined slightly below the surface of the microsphere, dueto repeated total internal reflection, thus resulting in very longcavity lifetimes and photon path lengths. Cavity Qs as high as 10¹⁰ havebeen reported.

[0014] The SPARROW optical waveguide includes a multi-layer dielectricstack disposed on the substrate, and a waveguide core. The dielectricstack includes alternating high and low refractive index dielectriclayers, and is highly reflective. The reflectivity of the dielectric issufficient to isolate the optical modes in the waveguide. The waveguidecore is substantially planar, and is disposed on the dielectric stack.The waveguide core extends along an axis, parallel to the waveguideplane, from an input end to an output end. The waveguide core is adaptedfor transmitting light incident on the input end to the output end.

[0015] An optical microcavity is constructed and arranged so as tooptically interact with light incident on the input end of the opticalwaveguide core. In one embodiment, the microcavity may be disposed alonga sensing axis, perpendicular to the waveguide plane. A flexure has afirst end coupled to the substrate, and a second end coupled to theoptical microcavity. The flexure is responsive to an input, such as anexternal force or acceleration, to cause a change in the couplinggeometry of the optical microcavity along the sensing axis.

[0016] The readout response of the sensor to an input can be determinedby measuring a variety of parameters, including but not limited to thecoupling gap, the resonance linewidth of the microcavity, the couplingstrength of the microcavity, and the resonant frequency of themicrocavity. Because of the high Qs of the microcavities, the resolutionand dynamic range of the sensor can be increased significantly. Sensorresolution of about 10⁻¹⁷ m and a dynamic range of about 10¹⁰ have beenattained for acceleration measurements.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1A illustrates a microcavity resonator accelerometer,constructed in accordance with the present invention.

[0018]FIG. 1B illustrates the microcavity displacement readout of theintegrated microcavity-waveguide accelerator shown in FIG. 1A.

[0019]FIG. 2 provides a cross-sectional view of an integratedmicrocavity-waveguide accelerometer, illustrating the microcavitydisplacement y in response to an applied load W.

[0020]FIG. 3A, 3B, and 3C provide graphs of the displacement of themicrocavity as a function of acceleration, for various lengths of thefiber stem.

[0021]FIG. 4 provides an overview of an experimental layout of amicrocavity resonator accelerometer, constructed in accordance with thepresent invention.

[0022]FIG. 5 is a table providing a summary of the microsphere resonatorreadout response analysis, in terms of readout resolution and dynamicrange, for different measurement techniques involving linewidth,coupling strength, and phase, respectively.

[0023]FIG. 6A illustrates the total cavity Q of the microcavity as afinction of the relative coupling gap between the waveguide and themicrocavity, in one exemplary embodiment of the present invention.

[0024]FIG. 6B illustrates the empirical parameters in an exemplarymicrocavity-waveguide coupler configuration.

[0025]FIG. 7 illustrates the coupling strength K as a function of thecoupling gap, in one exemplary embodiment of the present invention.

[0026]FIG. 8 illustrates a Mach Zehnder interferometer, as known in theprior art.

[0027]FIG. 9 illustrates a three-armed waveguide having a Mach-Zehndertype interferometric configuration, and adapted to couple light onto anoptical microcavity.

[0028]FIG. 10 illustrates the optical path difference l(d) for resonantlight propagating through an integrated microcavity interferometer,plotted as a function of the coupling gap.

[0029]FIG. 11 illustrates the phase change function Φ(d), as a functionof the coupling gap.

[0030]FIG. 12 is a table comparing the g-sensitivity of a microcavityresonator sensor, constructed in accordance with the present invention,with the g-sensitivity of other devices known in the art.

DETAILED DESCRIPTION

[0031] The present invention is directed to a high-resolution,miniaturized optical microcavity resonator sensor. The sensor is anintegrated optical system that includes a waveguide-coupled microcavityresonator. In particular, a SPARROW waveguide structure is used forevanescently coupling light into a high-Q optical microcavity, atextremely high efficiencies. The sensor is responsive to an input, suchas an external force, or to an environmental condition, such astemperature, to provide a very high-resolution readout.

[0032] A microcavity resonator sensor, constructed in accordance withthe present invention, may be used in a variety of inertial sensingapplications, including but not limited to ultra-high resolutiondisplacement readout, accelerometer, gyroscope, gravimeter, and seismicsensor. FIG. 1A illustrates one embodiment of an integratedmicrocavity-waveguide sensor 10, in accordance with the presentinvention. Optical microcavity resonators can be utilized as sensingdevices by monitoring perturbations of the evanescent field lightcoupling properties. In the illustrated embodiment, the sensor 10 is aflexure-based device. The potential displacement readout range of theaccelerometer 10 is from about 10⁻¹⁷ m to about 120 nm. Thecorresponding range of measurable acceleration is from about 3×10⁻¹⁰ gto about 3 g, although this range may be adjusted by varying the systemdesign parameters.

[0033] In overview, the system 10 includes a substrate, an opticalmicrocavity 20, and a waveguide chip 30 that is used to couple lightinto and out of the optical microcavity 20, all integrated into a singlestructure. The substrate is preferably substantially planar, and may bemade of silicon, by way of example. An optical source 50, preferably alaser, provides a beam 60 of input radiation directed to the waveguide.A photodetector 70 detects output optical radiation from the waveguide30.

[0034] In a preferred embodiment, the optical microcavity 20 is a fusedsilica microsphere or microring, fabricated from singlemode opticalfiber. The optical microcavity 20 may be fabricated by surface tensionshaping of the tip of freshly melted optical fiber. Melting of the tipof a silica wire or fiber may be accomplished through arcing in a fusionsplicer, or by means of a gas flame. In a preferred embodiment, thewaveguide chip 30 is a SPARROW waveguide deposited on a substrate 32,discussed in further detail below in conjunction with FIG. 1B. In theillustrated embodiment, integration of the microcavity 20 and thewaveguide chip 30 is accomplished using a fiber stem 40, which remainsattached to the optical microcavity 20, following the fabrication of themicrosphere. The fused silica fiber stem 40 functions as a small, stiffflexure. The fused silica microsphere functions as a proof mass.

[0035] In a preferred embodiment, the waveguide chip 30 is a SPARROWwaveguide, which provides an efficient and robust coupling mechanism forexciting whispering-gallery-modes in the optical microcavity 20, asdescribed in the CSLL-625 application. FIG. 1B illustrates a SPARROWwaveguide 310, constructed in accordance with the present invention. TheSPARROW waveguide 310 includes a multi-layer, high-reflectivitydielectric stack 330 disposed on the substrate 320, and a waveguide core340. The substrate 320 is substantially planar, and in one embodiment ismade of silicon.

[0036] The dielectric stack 330 is composed of alternating high (n_(H))and low (n_(L)) refractive index layers 331 and 332, made of adielectric material. As a result, the dielectric stack 330 functions asa high reflectivity dielectric mirror. The larger the number of layers331 and 332, the higher the reflectivity of the stack 130 becomes. Whilethe illustrated embodiment includes only one low index layer 332disposed between two high index layers 331, the number of the layers 331and 332 can be increased in order to increase the reflectivity of thestack 330. The alternating layers 331 and 332 forming the dielectricstack 330 provide a cladding for the SPARROW waveguide core 340, i.e.the layers forming the stack 330 may be regarded as cladding layers.

[0037] The high reflectivity of the dielectric stack 330 permitsisolation of the optical modes of the microcavity and the waveguide core340 from the waveguide cladding and the substrate. By isolating thewaveguide core 340 using the high-reflectivity dielectric stack 330, theSPARROW 310 circumvents the need for obtaining low refractive indexcladding materials. One of the high refractive index layers 331 is incontact with the substrate 320.

[0038] In one embodiment, the high refractive index layer 331 is made ofSi (silicon), while the low refractive index layer 332 is made of SiO₂(silica). In one embodiment, the high refractive index n_(H) is about3.5, and the low refractive index n_(L) is about 1.45, although otherrefractive indices are also within the scope of the present invention.The refractive indices required for efficiently guiding light within thewaveguide depend on the wavelength of optical radiation.

[0039] The waveguide core 340 is disposed on top of the dielectric stack330, and is in contact with another one of the high refractive indexlayers 331. The waveguide core 340 includes an input end 342 and anoutput end 344, and is adapted for transmitting optical radiationincident on the input end 342 to the output end 344. In one embodiment,the waveguide core is made of silica, and is characterized by the lowrefractive index n_(L).

[0040] As described earlier, the fused silica fiber stem 40 (shown inFIG. 1A) functions as a small, stiff flexure. Referring back to FIG. 1A,the flexure 40 has a first end 41 coupled to the substrate 32, and asecond end 42 arranged to interact with the optical microcavity 20. Theflexure 40 is responsive to an input, such as acceleration by way ofexample, to cause a change in the coupling geometry between themicrocavity 20 and the optical waveguide 30.

[0041]FIG. 1C illustrates the microcavity displacement readout of theintegrated microcavity-waveguide sensor 10 shown in FIG. 1. The stem 20is bonded to the chip surface in a way such that the coupling gap dbetween the microcavity 20 and the waveguide 30 is less than 1 μm, i.e.within the range for evanescent light coupling between the waveguide 30and the microcavity 20. When bonded to the chip surface, the fiber stem20 functions as a flexure for the microsphere readout. A force appliedalong the microsphere-waveguide coupling axis, shown in FIG. 1B as 22,therefore results in a displacement of the microcavity 20 relative tothe waveguide 30, and a corresponding change in the coupling gap. Amicrocavity positioner 61 and a waveguide positioner 63 may be used toposition the microcavity and the waveguide.

[0042] In an exemplary embodiment, a fiber stem approximately 50 μm indiameter and a microsphere approximately 200 μm in diameter may beintegrated with the waveguide 30. The fiber stem 20 may be anchored tothe waveguide surface, using epoxy, by way of example. In oneembodiment, the microsphere may be attracted to the surface byelectrostatic forces, and may be positioned above the waveguide channelusing rails fabricated into the waveguide chip.

[0043]FIG. 2 provides a cross-sectional view of the integratedmicrocavity-waveguide accelerometer, illustrating the microcavitydisplacement y in response to an applied load W. If themicrocavity/fiber-stem system is approximated as a point load at the endof a beam, treating the microcavity as a proof mass, the microcavitydisplacement y resulting from applied force$W = {\rho \frac{\pi}{6}d^{3}}$

[0044] α is given by $y = \frac{W\quad l^{3}}{3\quad E\quad I}$

[0045] where

[0046] I is the area moment of inertia of the fiber stem$( {I = \frac{\pi \quad D^{4}}{64}} ),$

[0047] d is the microsphere diameter,

[0048] l is the fiber stem length,

[0049] D is the fiber stem diameter,

[0050] ρ is the density of fused silica (2.2×10³ kg/m³),

[0051] and E is the bulk modulus of fused silica (7×10¹⁰ N/m²).

[0052]FIG. 3A, 3B, and 3C provide plots of the displacement of themicrocavity as a function of acceleration for various lengths of thefiber stem. The displacement y is plotted in these figures as a functionof proof mass acceleration for nominal values of the microsphere andfiber stem parameters, namely a 300 μm diameter microsphere, and a 125μm diameter fiber stem. Several fiber stem lengths are used in order toillustrate the device response for a range of flexure lengths, namely 1mm for FIG. 3A, 5 mm for FIG. 3B, and 1 cm for FIG. 3C.

[0053]FIG. 4 provides an overview of an experimental layout of amicrocavity resonator accelerometer 100, constructed in accordance withthe present invention. An optical source 101, preferably a laser,generates incident light directed at an input end 105 of a SPARROWwaveguide 114. The laser 101 is preferably a narrowband tunableexternal-cavity diode laser emitting light at a wavelength 1.55 μm, witha fiber-coupled output of greater than 10 mW. Both fine and coarsetuning modes may be available for the laser 101. Typically, a maximumfine-tuning range of 30 GHz is sufficient to observe several microsphereresonances. A microcavity 110, formed at an end of a fiber stem 111 , ispositioned within an evanescent coupling distance of a SPARROW couplingwaveguide 114. A collimating lens 117 is provided for collimating outputoptical radiation transmitted through the waveguide 109. Output opticalradiation is detected by photodetectors 122. Ultra-high resolutionnano-positioners 120 are provided for relative positioning of the fiberstem 111, coupling waveguide 114, microcavity 110, and the outputcoupling lens 117. With active feedback control, these piezo-drivenpositioners 120 can achieve 5 nm positioning resolution.

[0054] In one embodiment, the microcavity 110 and the waveguide 114 maybe mounted on separate positioners, prior to the microcavity/waveguideintegration step. The position of the microcavity 110 can be manipulatedthrough the fiber stem 111, which preferably remains attached to themicrocavity 110, following microsphere fabrication. In one form of theinvention, a high-finesse etalon 125 can be utilized for frequencycalibration of system parameters such as resonance linewidths. Theetalon 125 may have a 150 MHz free spectral range, and less that 2 MHzresolution, by way of example. For wavelength calibration over largewavelength/frequency ranges, a Burleigh wavelength meter may be used.The Burleigh wavelength meter uses a frequency-stabilized HeNe laser toprovide frequency accuracy to 30 MHz. In the illustrated embodiment ofthe invention, lock-in amplifiers 130 are used to lock the laserfrequency to a microsphere resonance, and to measure resonant frequencyshifts.

[0055] In a preferred embodiment of the present invention, the sensor isresponsive to an inertial input, such as an external force oracceleration, to determine variables such as acceleration, distance, andvelocity, by measuring the change in the coupling gap between themicrocavity and the waveguide. The inertial input, preferably appliedalong the microsphere-waveguide coupling axis, results in a displacementof the microcavity 20 relative to the waveguide 30, and a correspondingchange in the coupling gap.

[0056] There are several parameters which can be used to measure themicrocavity readout response indicating the change in coupling gap:resonant frequency of the microsphere, resonance linewidth of themicrosphere, coupling strength, also referred to as fractional depth,and phase. These parameters can all be used to monitor changes in themicrosphere cavity Q induced by some form of coupled-mode perturbation.FIG. 5 is a table providing a summary of the microsphere resonatorreadout response analysis, in terms of readout resolution and dynamicrange, for different measurement techniques involving linewidth,coupling strength, and phase, respectively. A description of thesetechniques is given below.

[0057]FIG. 6A illustrates the total cavity Q of the microcavity, in oneexemplary embodiment of the present invention. In FIG. 6A, the totalcavity Q(d) is plotted as a function of the relative coupling gapQ_(c)(d) between the waveguide 30 and the microcavity 20. The Q isdefined as ν/Δν, where ν is the resonant frequency and Δν is thelinewidth. The cavity Q(d) of the microcavity resonator is thereforetypically determined by measuring the cavity resonance linewidth Δν.

[0058] The linewidth Δν may be expressed as a function of thedisplacement d between the microcavity and the waveguide, the intrinsiccavity Q₀, and empirical parameters including the microcavity radius a,the laser wavelength λ, and the index of refraction n of the fusedsilica microcavity. These empirical parameters are illustrated in FIG.6B, which depicts the basic coupling configuration between a microsphere200 and a waveguide 202, separated by a coupling gap d.

[0059] The coupling parameter Q_(c), also called the loading parameter,can be approximated analytically as a function of the coupling gap,$\begin{matrix}{{Q_{c}(d)} = {102( \frac{a}{\lambda} )^{\frac{5}{2}}\frac{n^{3}( {n^{2} - 1} )}{{4q} - 1}^{2\gamma \quad d}}} & {{Eq}.\quad 1}\end{matrix}$

[0060] where

[0061] a is the microsphere radius (taken to be 100 μm),

[0062] λ is the laser wavelength (1.55 μm),

[0063] n is the index of refraction of fused silica (1.46),

[0064] q is the radial mode number,

[0065] and γ is related to the wave number:$\gamma = {\frac{2\pi}{\lambda}{\sqrt{n^{2} - 1}.}}$

[0066] It is convenient to introduce a coefficient N(q) for Q_(c)(d).N(q) is a function of the radial mode number, and is given by:$\begin{matrix}{{N(q)} = {102( \frac{a}{\lambda} )^{\frac{5}{2}}{\frac{n^{3}( {n^{2} - 1} )}{{4q} - 1}.}}} & {{Eq}.\quad 2}\end{matrix}$

[0067] The total cavity Q of the microsphere can now be expressed as afunction of the coupling parameter Q_(c) (d), and the intrinsic Q, whichmay be denoted as Q₀: $\begin{matrix}{{Q(d)} = {\frac{Q_{0}{Q_{c}(d)}}{Q_{0} + {Q_{c}(d)}} = {\frac{Q_{0}}{1 + {\frac{Q_{0}}{N(q)}^{{- 2}\gamma \quad d}}}.}}} & {{Eq}.\quad 3}\end{matrix}$

[0068] Using equation 3, the WGM resonance linewidth may be expressed interms of the total cavity Q and the coupling gap d: $\begin{matrix}{{\Delta \quad {v(d)}} = {\frac{v}{Q(d)} = {\frac{v}{Q_{0}}{( {1 + {\frac{Q_{0}}{N(q)}^{{- 2}\gamma \quad d}}} ).}}}} & {{Eq}.\quad 4}\end{matrix}$

[0069] Since the microspheres are fabricated by surface tension shapingthe tips of freshly melted optical fiber, the shapes which are obtainedare not perfectly spherical, therefore many different radial and polarcavity modes may be observed within the fine-tuning modulation cycle.Each mode possesses a different linewidth and thus a different cavity Q.The laser frequency may be modulated, using its fine-tuning mechanism,across at least one microsphere resonance. If a high-Q mode is desired,then the mode with the most narrow resonance linewidth is selected. Inone form of the invention, the resonance linewidth may be measured by aTektronix digital oscilloscope using its width measurement feature.

[0070] The total cavity Q illustrated in FIG. 6A is obtained directlyfrom resonance linewidth measurements. FIG. 6A provides experimentalverification of the expression for Q(d) as provided in equation 3. Theexperimental measurements for FIG. 6A have been obtained by sweeping thefrequency of a narrowband laser source across a microsphere resonance,while piezoelectrically modulating the coupling gap. Radial mode numbersranging from 1 to 10 were then extracted from the data fits.

[0071] The coupling-gap resolution δd can be obtained using thederivative of equation 4, namely the resonance linewidth function withrespect to the coupling gap. The coupling-gap resolution δd can beexpressed as a function of the linewidth measurement resolution δΔν:$\begin{matrix}{{\delta \quad {d( {d,{{\delta\Delta}\quad v},q} )}} = {\frac{\delta \quad \Delta \quad {v(d)}}{d\quad \Delta \quad {{v(d)}/d}\quad d} = {\frac{N(q)}{2\gamma \quad v}^{2\gamma \quad d}{\delta\Delta}\quad v}}} & {{Eq}.\quad 5}\end{matrix}$

[0072] Since the linewidth function is exponential for smalldisplacements, there is no maximum linewidth. It can therefore be seenfrom equation 5 above that the greatest sensitivity is obtained for thesmallest possible bias coupling gaps. In one exemplary embodiment, thebias displacement may be about 100 nm, and the linewidth measurementresolution may be about 0.1 MHz. For a 100 nm bias position, the rangeof near-linearity of the linewidth is approximately 35 nm, to withinabout 1%. The displacement resolution for the radial mode number q=1 istherefore 5.68×10⁻⁴ microns. For q=10, the displacement resolutionbecomes 4.37×10⁻⁴ microns. A reasonable value for the lower limit of thedisplacement measurement range is therefore 0.44 nm. Since the upperlimit of the measurement range is given by the maximum detectableseparation (approximately 1 μm), the dynamic range is approximately2000. When only the region of near-linearity is considered, the dynamicrange is reduced to ≈100.

[0073] Another parameter which can be measured and used as an indicatorof coupler-microsphere separation is the coupling strength, alsoreferred to as the fractional depth. FIG. 7 illustrates the couplingstrength K as a function of the coupling gap, in one exemplaryembodiment of the present invention. The coupling strength K can beexpressed as a function of the coupling parameter Q_(c)(d) and intrinsicQ, and therefore the coupling gap d: $\begin{matrix}{{K( {d,q} )} = {\frac{4Q_{0}{Q_{c}(d)}\Gamma^{2}}{( {Q_{0} + {Q_{c}(d)}} )^{2}} = \frac{4Q_{0}{N(q)}^{2\gamma \quad d}\Gamma^{2}}{( {Q_{0} + {{N(q)}^{2\gamma \quad d}}} )^{2}}}} & {{Eq}.\quad 6}\end{matrix}$

[0074] In equation 6, Γ describes the mode matching between the couplerand the microsphere; Γ=1 corresponds to a perfect, ideal mode matchingcondition. A very conservative estimate for the Γ value is 0.8, giventhat coupling strengths as high as 98% have been observed.

[0075] In order to maximize the measurement sensitivity, thecoupler-microsphere separation should be biased at the location of themaximum derivative of the coupling strength K with respect to thecoupling gap, in order to maximize the measurement sensitivity. Theselocations can be obtained by finding the roots of the second derivativeof K with respect to coupling gap (for q=1, d₁=0.22 μm and d₂=0.52 μm).The maximum resolution of this measurement technique is determined usingthe maximum slope of K (2.124 μm⁻¹): $\begin{matrix}{{\delta \quad d} = \frac{\delta \quad K}{{K}/{d}}} & {{Eq}.\quad 7}\end{matrix}$

[0076] if the fractional depth measurement resolution δK is 10⁻⁶(obtained using dual-beam, Shot-noise limited detection techniques),then the displacement resolution δd is 4.7×10⁻¹³ m.

[0077] The dynamic range of the displacement measurements is given bythe range of the depth measurements: the lower limit is equal to thedisplacement resolution when biased at the maximum slope of K, and theupper limit is approximately equal to the maximum detectable separation(≈1 μm). The dynamic range is therefore approximately 10⁶. Thecoupling-gap range for near-linearity of K (to within 1%) is 120 nm whenbiased at 0.22 microns, so the dynamic range corresponding to the regionof near-linearity is approximately 10⁵.

[0078] Because of the high Q and the long cavity lifetimes of theoptical microcavity, the sensor featured in the present invention has agreatly increased resolution and dynamic range, as compared to prior artsensors, such as MEMS accelerometers. Resolutions of up to about 1.0 nmhave been obtained, in a compact size comparable with MEMS sensors. Thisrepresents an improvement of several orders of magnitude, as comparedwith the prior art.

[0079] A third parameter which can be measured in order to obtain thecoupler-microsphere separation is phase. When the microsphere isintegrated into a waveguide having an interferometric configuration, theresonant light circulating within the microcavity gains phase withrespect to light in a reference channel of the interferometricwaveguide. The change in phase experienced by the resonant light can bemeasured by using a waveguide having an interferometric configuration,for example a waveguide including channels arranged in a Mach-Zehndertype interferometric configuration.

[0080]FIG. 8 illustrates a Mach-Zehnder interferometer 400, as known inthe prior art. As known in the art, an incoming optical signal 402 in aMach-Zehnder interferometer is split into two signals, E₁ and E₂, forexample at a Y-junction. Each signal enters a first waveguide branch 404and a second waveguide branch 406, respectively. The signals arerecombined into an output waveguide 410, which provides a modulatedoptical output signal, E₃ (E₃=E₁+E₂). The Mach-Zehnder modulator 400 istypically formed of materials that have a high electro-opticcoefficient, so that their refractive indices can be altered by applyingan electric field in that region. Typically, a modulation signal 407 isapplied to a modulator input electrode 408. The signal 407 causes anelectric field to be applied to one or both of the waveguide branches404 and 406. In accordance with the electro-optic effect, the appliedelectric field causes a change in the refractive index, corresponding tothe changing amplitude of the modulating signal. The change in the indexof refraction alters the speed of light in the region, resulting in achange in the delay time of the light passing through the region. Themodulation signal thus enables the optical path length in one or both ofthe waveguides branches to be controlled, so that a phase differenceresults between the two signals E₁ and E₂, when they are recombined atthe output waveguide 410.

[0081]FIG. 9 illustrates a three-armed waveguide 500 having aMach-Zehnder type interferometric configuration, and adapted to couplelight onto a microcavity 501. The waveguide 500 has an input end 510 andan output end 512. The interferometric waveguide 500 includes threewaveguide arms 505, 506, and 507. The first arm 505 forms an inputchannel, and is adapted to input coupling light into the microsphere.The second arm 506 forms a drop channel, and is adapted to out-couplelight from the microcavity into the waveguide. The third arm 507 is usedas a reference channel, which has substantially no interaction with themicrocavity.

[0082] At the output end 512, light from the reference channel 507 iscombined or interfered with light from the drop channel 506, i.e. lightthat has interacted with the microsphere. A displacement resolution of10⁻¹⁷ m can be achieved using this interferometric technique, with onlya moderate phase measurement resolution, as shown below.

[0083] The change in phase experienced by the resonant light may beexpressed in terms of the cavity lifetime τ(d) and optical pathdifference (OPD) l(d). The cavity lifetime τ(d) for resonant light canbe expressed as a function of the total cavity Q, and thus the couplinggap, $\begin{matrix}{{\tau (d)} = {\frac{Q(d)}{\omega} = \frac{\tau_{0}}{1 + {\frac{Q_{0}}{N(q)}^{{- 2}{\gamma d}}}}}} & {{Eq}.\quad 8}\end{matrix}$

[0084] where τ₀=Q₀/ω. Assuming interferometer arms of equal path length(not including the microsphere), the OPD l(d) can then be expressed as afunction of the cavity lifetime, $\begin{matrix}{{l(d)} = {{\frac{c}{n}{\tau (d)}} = {{\frac{\lambda}{2\pi \quad n}{Q(d)}} = {\frac{c\quad \tau_{0}}{n}\frac{1}{1 + {\frac{Q_{0}}{N(q)}^{{- 2}\gamma \quad d}}}}}}} & {{Eq}.\quad 9}\end{matrix}$

[0085]FIG. 10 illustrates the optical path difference l(d) for resonantlight propagating through an integrated microcavity interferometer,plotted as a function of the coupling gap. For large coupling gaps, theOPD can be very long, however for such coupling gaps, the couplingefficiency is very weak and therefore very few photons are coupled intothe cavity. The higher the Q of a cavity, the larger the propagationdistance within the microcavity.

[0086] The phase difference observed between light propagating withinthe microsphere and light propagating through the reference channel ofthe interferometer is given by $\begin{matrix}{{{\Delta\varphi}(d)} = {\frac{2\pi \quad n}{\lambda}{l(d)}}} & {{Eq}.\quad 10}\end{matrix}$

[0087] Substituting the expression for l(d) as a function of Q(d) fromequation 9 yields:

Δφ(d)=Q(d).  Eq. 11

[0088] The phase difference is thus linear to within about 1%, over a180 nm range centered around the location of maximum phase differenceslope.

[0089]FIG. 11 illustrates the phase change function Φ(d), which providesa measure of the sensitivity of the phase-based coupling-gap measurementtechnique. The sensitivity is determined using the phase differencechange resulting from a change in the optical path length. The phasechange function Φ(d) may be defined as the derivative with respect to dof${{{\Delta\varphi}(d)}:{\Phi (d)}} = {\frac{}{d}{{{\Delta\varphi}(d)}.}}$

[0090] Since Δφ(d)=Q(d), the phase change function can be given as afunction of the coupling gap d: $\begin{matrix}{{\Phi (d)} = \frac{2\gamma \frac{Q_{0}^{2}}{N(q)}^{{- 2}\gamma \quad d}}{( {1 + {\frac{Q_{0}}{N(q)}^{{- 2}\gamma \quad d}}} )^{2}}} & {{Eq}.\quad 12}\end{matrix}$

[0091] The maximum readout sensitivity is obtained when the device isbiased at the coupling gap which corresponds to the maximum value of thephase change function Φ(d). However, the bias point which corresponds tothe maximum range of near-linear response is the coupling gap whichprovides the maximum slope of Φ(d). Solving for the roots of the secondderivative of Φ(d) yields d=0.526 μm and 0.220 μm. The optimal phaseresponse is therefore Φ(0.22 μm)=1.44×10⁸ radians/micron. Assuming thephase resolution of the optical system to be 10⁻³ radians, thecorresponding displacement resolution is 10⁻¹¹ microns, or 10⁻¹⁷ meters.As with the other techniques, the upper limit of the dynamic range isapproximately equal to the maximum detectable separation (≈1 μm). Thedynamic range is therefore approximately 10¹¹. If only the linearportion of the phase change function is considered (≈120 nm range forlinearity to within 1%), the dynamic range is approximately 10¹⁰.

[0092] The range of accelerations which would correspond to anear-linear displacement sensitivity range of 10⁻¹⁷ m to 120 nm is fromabout 3×10⁻¹⁰ g to about 3 g. FIG. 12 is a table comparing theg-sensitivity of a microcavity resonator sensor, constructed inaccordance with the present invention, with the g-sensitivity ofexisting techniques, for several common acceleration environments.Because of the very stiff flexure provided in the present invention, theg-sensitivity of a microcavity resonator sensor, constructed inaccordance with the present invention, is significantly reduced, asshown in FIG. 12.

[0093] When the microcavity resonator sensor of the present inventioncombines the compact size of a MEMS device with a high resolution, byutilizing high-Q optical microcavity resonators, and SPARROW waveguidesthat allow for high coupling efficiencies. A significantly improveddynamic range is also achieved. Potential embodiments of the presentinvention include, but are not limited to, accelerometer, gyroscope,vibration meter, gravimeter, displacement sensor, velocity sensor,seismic sensor,

[0094] While the invention has been particularly shown and describedwith reference to specific preferred embodiments, it should beunderstood by those skilled in the art that various changes in form anddetail may be made therein without departing from the spirit and scopeof the invention as defined by the appended claims.

What is claimed is:
 1. An optical resonator sensor, comprising: A. asubstrate; B. an optical waveguide, comprising: (a) a multi-layerdielectric stack disposed on said substrate, said dielectric stackincluding alternating high and low refractive index dielectric layers;(b) a waveguide core disposed on said dielectric stack and having aninput end and an output end, said waveguide core being adapted fortransmitting light incident on said input end to said output end; C. anoptical microcavity disposed along a sensing axis; wherein said opticalmicrocavity is constructed and arranged so as to optically interact withsaid light incident on said input end of said optical waveguide core;and D. a flexure having a first end coupled to said substrate and asecond end arranged to interact with said optical microcavity, saidflexure being responsive to an input to cause a change in the couplinggeometry between said microcavity and said optical waveguide.
 2. Anoptical resonator sensor according to claim 1, wherein said change inthe coupling geometry includes a displacement of said opticalmicrocavity along said sensing axis, and wherein said displacement ofsaid optical microcavity is proportional to said inertial input.
 3. Anoptical resonator sensor according to claim 1, wherein said opticalmicrocavity is disposed at a distance from said optical waveguide thatis sufficiently small so as to allow evanescent coupling between saidmicrocavity and said optical waveguide.
 4. An optical resonator sensoraccording to claim 3, wherein said distance is less than one wavelengthof said optical radiation propagating through said optical waveguide. 5.An optical resonator sensor according to claim 3, wherein saidevanescent field is characterized by a frequency substantially equal toa resonant mode of said optical microcavity.
 6. An optical resonatorsensor according to claim 5, wherein said resonant mode of said opticalmicrocavity is a whispering gallery mode.
 7. An optical resonator sensoraccording to claim 6, wherein said optical microcavity has asubstantially spherical shape, and wherein the wavelengths of thewhispering gallery modes of said microcavity are about λ and integermultiples thereof, λ being related to the radius r of said substantiallyspherical microcavity according to the formula: 2πr=nλ, and n is anonzero integer.
 8. An optical resonator sensor according to claim 1,wherein said first dielectric layer comprises silicon.
 9. An opticalresonator sensor according to claim 1, wherein said second dielectriclayer and said waveguide core layer comprises silica.
 10. An opticalresonator sensor according to claim 1, wherein said optical microcavityis selected from the group consisting of microspheres, microdisks, andmicrorings.
 11. An optical resonator sensor according to claim 1,wherein said optical microcavity is made of silica.
 12. An opticalresonator sensor according to claim 1, wherein said change comprises achange in the resonance linewidth of at least one resonant mode of saidoptical microcavity.
 13. An optical resonator sensor according to claim1, wherein said change comprises a change in the resonance frequency ofat least one resonant mode of said optical microcavity.
 14. An opticalresonator sensor according to claim 1, wherein said change comprises achange in the coupling strength between said optical microcavity andsaid optical waveguide core.
 15. An optical resonator sensor accordingto claim 1, wherein said change comprises a change in the cavity Q ofsaid optical microcavity.
 16. An optical resonator sensor according toclaim 1, further comprising a light source arranged to input light intosaid input end of said optical waveguide.
 17. An optical resonatorsensor according to claim 1, further comprising at least one detectorconstructed and arranged so as to detect output optical radiation fromsaid output end of said optical waveguide.
 18. An optical resonatorsensor according to claim 1, wherein said optical microcavity is made ofsilica.
 19. An optical resonator sensor according to claim 1, whereinsaid optical waveguide is an integrated optical chip.
 20. An opticalresonator sensor according to claim 1, wherein the coupling efficiencyof said evanescent field into said optical microcavity is from about 95%to about 99.99%.
 21. An optical resonator sensor according to claim 1,wherein the reflectivity of said dielectric stack is sufficient toisolate the optical modes within said waveguide core from saidsubstrate.
 22. An optical resonator sensor according to claim 1, whereinthe reflectivity of said dielectric stack is sufficient to isolate theoptical modes in said microcavity from said substrate.
 23. An opticalresonator sensor according to claim 1, wherein said optical microcavityis fabricated by melting one end of an optical fiber.
 24. An opticalresonator sensor according to claim 1, wherein said optical microcavityis characterized by a quality factor (Q) from about 10⁹ to about 10¹⁰.25. An optical resonator sensor according to claim 1, wherein saidoptical microcavity is characterized by a diameter of about 50 μm toabout 500 μm.
 26. An optical resonator sensor according to claim 1,wherein said optical microcavity is characterized by a diameter of about200 μm.
 27. An optical resonator sensor according to claim 1, whereinsaid high refractive index is about 3.5, and said low refractive indexis about 1.45.
 28. An optical resonator sensor according to claim 1,wherein the thickness and the width of said waveguide core is chosen soas to provide an effective refractive index for said waveguide core thatmatches the refractive index of said microcavity when a resonant WGMmode is excited therewithin.
 29. An optical resonator sensor accordingto claim 28, wherein said thickness of said waveguide core is about 2.0μm, said width of said waveguide is about 6.0 μm, and said effectiverefractive index for said waveguide core is about 1.40.
 30. An opticalresonator sensor according to claim 1, wherein said optical waveguidecomprises: a splitter for splitting said input optical radiation into afirst signal and a second signal; a first waveguide branch and a secondwaveguide branch for transmitting said first signal and said secondsignal, respectively; and a combiner for recombining said first signaland said second signal.
 31. An optical resonator sensor according toclaim 30, wherein said optical waveguide includes channels arranged in aMach-Zehnder interferometer configuration.
 32. An optical resonatorsensor according to claim 30, wherein said optical waveguide coreincludes a drop channel, a throughput channel, and a reference channel,arranged so that the optical microcavity can optically interact withboth the drop channel and the throughput channel, but does notsubstantially optically interact with light in the reference channel.33. An optical resonator sensor according to claim 1, wherein said inputcomprises at least one of external force, acceleration, pressure, shear,and strain.
 34. An optical resonator sensor according to claim 1,wherein said substrate is in contact with one of said low refractiveindex layers, and wherein said waveguide core is in contact with a oneof said high refractive index layers.
 35. An optical resonator sensorcomprising: (a) a substrate; (b) an optical waveguide disposed on thesubstrate and having an input end and an output end; (c) an opticalmicrocavity constructed and arranged so as to optically interact withlight incident on said input end of said optical waveguide; and (d). aflexure having a first end coupled to said substrate and a second endarranged to interact with said optical microcavity and to move inresponse to an environmental condition and thereby change the opticalmicrocavity interaction with light in the optical waveguide.
 36. Anoptical resonator sensor according to claim 35, wherein saidenvironmental condition comprises temperature.
 37. An optical resonatorsensor according to claim 1, wherein said waveguide core extends withina waveguide plane and along an axis from an input end to an output end,said axis being parallel to said waveguide plane; and wherein saidsensing axis is perpendicular to said waveguide plane.
 38. An opticalresonator sensor, comprising: A. a substrate; B. an optical waveguide,comprising: (a) a multi-layer dielectric stack disposed on saidsubstrate, said dielectric stack including alternating high and lowrefractive index dielectric layers; (b) a waveguide core disposed onsaid dielectric stack and having an input end and an output end, saidwaveguide core being adapted for transmitting light incident on saidinput end to said output end; C. an optical microcavity constructed andarranged so as to optically interact with said light incident on saidinput end of said optical waveguide core; and D. a flexure having afirst end coupled to said substrate and a second end arranged tointeract with said optical microcavity and arranged to move the opticalmicrocavity in response to one of an input and an environmentalcondition.